Table of Fifths

PLEASE NOTE that, while uploading, the links in the table have been disabled - in case difficulty is encountered with the upload of the 112 images.

Open this page in two windows, and then size one of the windows so that it occupies the left half of the screen with this paragraph visible, and then scroll down the other one to the middle of the table - where the row is the tall one with the names of the modes, Ionian, Dorian, Phrygian etc. Please do not click on any of the links in the table until asked to do so below.

WITH YOUR INDEX FINGER ONLY:

(1) Play all the white keys from   C   to the next   C,   and imagine that, when you get to the end of the row, you look back to the beginning of the row to find the second   C   -   but you still played higher. You did not go back to the first   C   on the keyboard when you looked again at the   C   in the table. You have just played the Ionian mode.

(2) Play all the white keys from   D   to the next   D.   This time look to the beginning of the row to find the last two notes,   C   and the second   D.   You have just played the Dorian mode.

(3) Play all the white keys from   E   to the next   E.   This time look to the beginning of the row to find the last three notes,   C, D   and the second   E.   You have just played the Phrygian mode.

Now think of the seven modes as a group of three followed by a group of four, and repeat the above exercise for each of the modes in the group of four.

MAJOR KEYNOTES ON THE CIRCLE OF FIFTHS

Find and look at the circle of fifths, and note that the top part of the first column in the table gives the keynotes for the major scales that have signature keys with flats. Similarly, the bottom part of the first column in the table gives the keynotes for the major scales that have signature keys with sharps.

MINOR KEYNOTES ON THE CIRCLE OF FIFTHS

Similarly, note that the top part of the Aeolian column gives the keynotes for the minor scales on the circle of fifths that have signature keys with flats. And the bottom part of the Aeolian column gives the keynotes for the minor scales on the circle of fifths that have signature keys with sharps.

TONE AND SEMI-TONE

For the purpose of playing scales with the help of this page, the term semi-tone means precisely, and absolutely nothing more than, the following: From any given key on the piano keyboard, a semi-tone higher is the next key to the right. For examples: D to D#, and B to C, and E to F. A semi-tone lower is the preceeding key to the left. For examples: A to Ab, and F to E. A tone is two semi-tones, so to go a tone higher or lower you skip a key to the right or left. For examples: G to A, and Gb to Ab, and B to C#, and Eb to F.

FIFTHS AND CONSTRUCTING THE TABLE

As we go around the circle of fifths in the clockwise direction, the major keynotes are separated one from the next by fifths - which experience tells me is equal to seven semi-tones. So to get from   C   to   G   I strike   C   counting it as zero, and then I play the next seven keys counting from one to seven. The same is true of the minor keynotes. If we go counter clockwise, then we go seven semi-tones lower in a similar manner.

The second column of the table was filled starting from the   D   in the center and counting seven semi-tone intervals: Lower for the flats in the upward direction of the table and higer for the sharps in the downward direction of the table. The rest of the columns were also filled by this process.

Just as each element of the Ionian or Aeolian columns is the starting note for a major or minor scale, so also is each element of the other columns a starting note for a scale. Ostensibly then there are 7 (columns) times 15 (rows) equals 105 scales. Because of the duplication which can be seen in the bottom three elements of the circle of fifths, what we are talking about here is 105 ways to write down 84 distinct scales.

I was quite surprised to find after completing the table that the keynotes actually show the scales when we look at the rows. We can play all the scales with one basic technique, as described next.

FINGERING TO TWO SWITCHES, 3 AND 4

Please scroll to the top of the table, and use the fingering that is shown there to play the C-major scale which can be seen in the tall middle row: C, D, E, F, G, A, B, C. Remember to go around the end of the row to its beginning to find the second   C   - but play it higher on the piano. This will be very important for playing the other scales.

The symbol   3↔1   separates the groups of three and four modes. This represents the switch from the middle finger to the thumb - when playing a scale in the increasing pitch direction, and it represents the switch from the thumb to the middle finger - when playing a scale in the decreasing pitch direction. Similarly, the symbol   4↔1   represents the switch from the ring finger to the thumb - when playing a scale in the increasing pitch direction, and it represents the switch from the thumb to the ring finger, when playing a scale in the decreasing pitch direction.

WHEN PLAYING THE SCALES, THE SEMI-TONES ALWAYS OCCUR AT THESE SWITCHES. EVERYWHERE ELSE, THE INTERVAL BETWEEN ADJACENT NOTES IN THE TABLE IS A TONE. This means that we always skip a key when going from one note to the next, UNLESS WE ARE AT ONE OF THE SWITCHES. If we are at one of the switches, then we do not skip a key.

Now pick any entry in the table. This will be the keynote (starting note) for a scale in the mode given by the column. The first note should be played with the finger shown at the top and bottom of the column. Looking to the right, NOTE WELL WHAT THE NEXT SWITCH WILL BE, and play JUST ONE OCTAVE accordingly.

PLAYING ANY MODE STARTING ON ANY KEY

I simply remember which finger to start on and which switch is next. For the first three modes, I hold up my thumb and first two fingers on my right hand - and visualize the table where these three modes precede the   3↔1   switch. For the last four modes, I hold up my thumb and first three fingers on my right hand - and visualize the table where these four modes precede the   4↔1   switch.

PLAYING ANY MODE WITH A SPECIFIED SIGNATURE KEY

Here, I use the memory device, described earlier in this diary at 10 December 2010, to find the major scale keynote which has the specified signature key. Then I play that major scale up to the note on which the number of the mode and the number of the note in the major scale are the same. For example, the Dorian mode is mode 2, and the the required key note is the second note in the major scale.

EXERCISE

In a new window, please scroll to the bottom of the table with links here so that only the bottom half of the table is visible.

I would like to present an exercise which I have found to be very helpful. I seem to be very absent minded, and very often I forget which switch is next. This happens most often when I am playing a scale in the decreasing pitch direction, but it also happens when playing scales in the increasing pitch direction.

I start with the Mixolydian scale that has the white keys G1, A1, B1, C2, D2, E2, F2, and G2. I put blocks on the keys as shown in the picture immediately below. These blocks come from the game "Risk" which I was given as a child in the 1960s. Small colored post-it notes would also work. I use a second color for the second instance of the keynote.

First, I play this one scale repeatedly until I can play it without pauses - all the notes being played for the same amount of time. In particular, I find it necessary to focus intently on the fact that the   4↔1   switch occurs at the right hand side of the three black key set, in both the upward and downward pitch directions. The   3↔1   switch occurs at the right hand side of the two black key set.

Then, I play the scale repeatedly from the lowest   G   on the piano to the highest   G.   HOWEVER, since each mode has its own distinct sound which I want to hear, I play the keynote twice at the octave boundaries - once to complete the lower octave, and once to begin the higher octave. Again I find it helpful to focus intently on where the switches occur.

Now do what your browser requires to create a new tab when you click on the Mixolydian G at the bottom of the tall row that has the mode names. Make the image full size and scroll it all the way to the left.

When I can play this scale confidently, I go on to the Aeolian scale. Make another new tab for this scale's image. By going back and forth repeatedly between the two new tabs, you can see that the new placement of the blocks is produced as follows: Pick up the lowest red block, and put it in place of the yellow one, which is then moved to a position that is one octave above the position of the new lowest red block. The changes can be seen in the picutres below, but the tab descriptions are included for viewing all the rest of the scales.

Natural Mixolydian
G

Natural Aeolian
A

Continuing through the natural scales, we end on   F.   This is convenient because the only change that is needed to get to the F# scale of the next row is to change   F   to   F#   - after which change I step down two scales to the Mixolydian D, so that we will finish on   C   - to again take advantage of a one sharp change from   C   to   C#.

This process moves the scales that we look at all the way up the keyboard. In fact, the two steps back taken at the beginning of each new row prevents us from running out of space. I like to think of this upward motion as being a consequence of sharps taking us higher. We will end at   F#   in the bottom row of the table:

7 sharp Lydian
F#

Making all the sharps natural takes us to the natural scale that is shown at the top of the tall Lydian cell of the table:

Natural Lydian
F

Before starting the downward progression of scales in each row of the upper half of the table, I go up two steps - so that each row will end on the Locrian mode. In the natural row, this will make   B   the last keynote (mouse over the links to see the numbering of the images in the status bar), and the transition to the 1-flat row will be made by changing   B   to   Bb - followed by a two step up (mouse over the links again to see the numbering). Again this keeps us from going beyond the bottom of the keyboard, and it enables us to make the single change to go from each row to the next.





















Table of Fifths
   
THUMB
INDEX
MID
  3↔1  
THUMB
INDEX
MID
RING
  4↔1  
   
  1  
  2  
  3  
  3↔1  
  1  
  2  
  3  
  4  
  4↔1  
  7b  
  Cb  
  Db  
  Eb  
  3↔1  
  Fb  
  Gb  
  Ab  
  Bb  
  4↔1  
  6b  
  Gb  
  Ab  
  Bb  
  3↔1  
  Cb  
  Db  
  Eb  
   F   
  4↔1  
  5b  
  Db  
  Eb  
   F   
  3↔1  
  Gb  
  Ab  
  Bb  
   C   
  4↔1  
  4b  
  Ab  
  Bb  
   C   
  3↔1  
  Db  
  Eb  
   F   
   G   
  4↔1  
  3b  
  Eb  
   F   
   G   
  3↔1  
  Ab  
  Bb  
   C   
   D   
  4↔1  
  2b  
  Bb  
   C   
   D   
  3↔1  
  Eb  
   F   
   G   
   A   
  4↔1  
  1b  
   F   
   G   
   A   
  3↔1  
  Bb  
   C   
   D   
   E   
  4↔1  
   
 C 

   Ionian   

 C   
 D 

   Dorian   

 D   
 E 

  Phrygian  

 E   
  3↔1  
 F 

   Lydian   

 F   
 G 

 MixoLydian 

 G   
 A 

   Aeolian   

 A   
 B 

   Locrian  

 B   
  4↔1  
  1#  
   G   
   A   
   B   
  3↔1  
   C   
   D   
   E   
  F#  
  4↔1  
  2#  
   D   
   E   
  F#  
  3↔1  
   G   
   A   
   B   
  C#  
  4↔1  
  3#  
   A   
   B   
  C#  
  3↔1  
   D   
   E   
  F#  
  G#  
  4↔1  
  4#  
   E   
  F#  
  G#  
  3↔1  
   A   
   B   
  C#  
  D#  
  4↔1  
  5#  
   B   
  C#  
  D#  
  3↔1  
   E   
  F#  
  G#  
  A#  
  4↔1  
  6#  
  F#  
  G#  
  A#  
  3↔1  
   B   
  C#  
  D#  
  E#  
  4↔1  
  7#  
  C#  
  D#  
  E#  
  3↔1  
  F#  
  G#  
  A#  
  B#  
  4↔1  
   
  1  
  2  
  3  
  3↔1  
  1  
  2  
  3  
  4  
  4↔1  
   
THUMB
INDEX
MID
  3↔1  
THUMB
INDEX
MID
RING
  4↔1  

For this table by itself on a page, suitable for printing, please click here.